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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_Simple Regression Y ~ X.wasp
Title produced by softwareSimple Linear Regression
Date of computationThu, 31 May 2012 08:16:04 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/31/t1338466582xx2j5ygd5ykqezi.htm/, Retrieved Mon, 06 May 2024 13:24:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168070, Retrieved Mon, 06 May 2024 13:24:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Simple Linear Regression] [davis data set ] [2012-05-31 12:16:04] [718abb62a78e84b22e01bdba2059eb20] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0	2
7	2
-1	3
-2	2
0	2
0	5
-1	2
-4	6
0	3
1	1
-5	1
1	3
-1	3
0	3
-5	3
-1	1
-9	2
0	3
1	-3
0	4
-5	2
0	0
-1	2
-4	3
-5	3
0	1
2	1
-2	6
-2	4
1	3
0	1
2	3
3	0
0	3
5	-1
-1	1
2	1
0	3
2	3
-2	-1
1	4
0	0
4	4
-2	3
3	4
-1	2
-2	1
0	4
-3	-1
-1	2
1	-1
-5	0
1	4
-1	3
5	3
-1	3
-1	0
0	7
-5	5
3	4
-1	4
1	2
1	2
2	3
1	3
4	3
1	4
0	-2
1	2
-1	4
0	5
-5	10
-1	2
-1	2
-1	0
1	2
-1	-2
1	-6
5	4
0	0
-2	-1
-4	3
0	0
-2	3
1	2
2	3
0	0
-2	1
-2	0
1	4
-1	5
2	3
0	4
0	6
0	1
0	3
0	3
0	3
-1	2
2	4
1	2
2	3
0	1
4	3
-6	0
0	8
-2	3
0	0
-1	2
0	5
0	3
2	1
-1	4
-1	0
1	3
-4	2
0	3
0	2
0	4
0	2
0	2
1	3
-2	0
3	2
3	0
-1	2
0	2
2	4
-1	3
2	3
-2	0
-1	3
-2	2
-1	0
-2	0
0	5
0	0
4	-1
3	3
2	1
-1	3
0	2
2	-2
4	3
-4	4
1	-2
1	2
1	3
0	1
1	4
1	1
-2	2
0	4
1	2
0	1
1	3
3	3
1	4
0	0
-2	0
3	0
-1	5
-1	3
0	1
2	1
4	5
0	0
0	2
5	4
4	3
1	3
1	3
-5	-3
3	0
0	-1
0	-2
1	3
3	0
3	0
-1	3
-2	-1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168070&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168070&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168070&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)0.020.2450.0840.934
X0.0010.0830.0090.993
- - -
Residual Std. Err. 2.313 on 179 df
Multiple R-sq. 0
Adjusted R-sq. -0.006

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 0.02 & 0.245 & 0.084 & 0.934 \tabularnewline
X & 0.001 & 0.083 & 0.009 & 0.993 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 2.313  on  179 df \tabularnewline
Multiple R-sq.  & 0 \tabularnewline
Adjusted R-sq.  & -0.006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168070&T=1

[TABLE]
[ROW][C]Linear Regression Model[/C][/ROW]
[ROW][C]Y ~ X[/C][/ROW]
[ROW][C]coefficients:[/C][C] [/C][/ROW]
[ROW][C] [/C][C]Estimate[/C][C]Std. Error[/C][C]t value[/C][C]Pr(>|t|)[/C][/ROW]
[C](Intercept)[/C][C]0.02[/C][C]0.245[/C][C]0.084[/C][C]0.934[/C][/ROW]
[C]X[/C][C]0.001[/C][C]0.083[/C][C]0.009[/C][C]0.993[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]2.313  on  179 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]-0.006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168070&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168070&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)0.020.2450.0840.934
X0.0010.0830.0090.993
- - -
Residual Std. Err. 2.313 on 179 df
Multiple R-sq. 0
Adjusted R-sq. -0.006






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
DHt10000.993
Residuals179957.9115.351 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
DHt & 1 & 0 & 0 & 0 & 0.993 \tabularnewline
Residuals & 179 & 957.911 & 5.351 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168070&T=2

[TABLE]
[ROW][C]ANOVA Statistics[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]Sum Sq[/C][C]Mean Sq[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C]DHt[/C][C]1[/C][C]0[/C][C]0[/C][C]0[/C][C]0.993[/C][/ROW]
[ROW][C]Residuals[/C][C]179[/C][C]957.911[/C][C]5.351[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168070&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168070&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
DHt10000.993
Residuals179957.9115.351


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = TRUE ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = TRUE ;
R code (references can be found in the software module):
par3 <- 'TRUE'
par2 <- ''
par1 <- ''
cat1 <- as.numeric(par1)
cat2<- as.numeric(par2)
intercept<-as.logical(par3)
x <- t(x)
xdf<-data.frame(t(y))
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
xdf <- data.frame(xdf[[cat1]], xdf[[cat2]])
names(xdf)<-c('Y', 'X')
if(intercept == FALSE) (lmxdf<-lm(Y~ X - 1, data = xdf) ) else (lmxdf<-lm(Y~ X, data = xdf) )
sumlmxdf<-summary(lmxdf)
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
nc <- ncol(sumlmxdf$'coefficients')
nr <- nrow(sumlmxdf$'coefficients')
a<-table.row.start(a)
a<-table.element(a,'Linear Regression Model', nc+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, lmxdf$call['formula'],nc+1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'coefficients:',1,TRUE)
a<-table.element(a, ' ',nc,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',1,TRUE)
for(i in 1 : nc){
a<-table.element(a, dimnames(sumlmxdf$'coefficients')[[2]][i],1,TRUE)
}#end header
a<-table.row.end(a)
for(i in 1: nr){
a<-table.element(a,dimnames(sumlmxdf$'coefficients')[[1]][i] ,1,TRUE)
for(j in 1 : nc){
a<-table.element(a, round(sumlmxdf$coefficients[i, j], digits=3), 1 ,FALSE)
}
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, '- - - ',1,TRUE)
a<-table.element(a, ' ',nc,FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Std. Err. ',1,TRUE)
a<-table.element(a, paste(round(sumlmxdf$'sigma', digits=3), ' on ', sumlmxdf$'df'[2], 'df') ,nc, FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R-sq. ',1,TRUE)
a<-table.element(a, round(sumlmxdf$'r.squared', digits=3) ,nc, FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-sq. ',1,TRUE)
a<-table.element(a, round(sumlmxdf$'adj.r.squared', digits=3) ,nc, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Statistics', 5+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',1,TRUE)
a<-table.element(a, 'Df',1,TRUE)
a<-table.element(a, 'Sum Sq',1,TRUE)
a<-table.element(a, 'Mean Sq',1,TRUE)
a<-table.element(a, 'F value',1,TRUE)
a<-table.element(a, 'Pr(>F)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, V2,1,TRUE)
a<-table.element(a, anova.xdf$Df[1])
a<-table.element(a, round(anova.xdf$'Sum Sq'[1], digits=3))
a<-table.element(a, round(anova.xdf$'Mean Sq'[1], digits=3))
a<-table.element(a, round(anova.xdf$'F value'[1], digits=3))
a<-table.element(a, round(anova.xdf$'Pr(>F)'[1], digits=3))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residuals',1,TRUE)
a<-table.element(a, anova.xdf$Df[2])
a<-table.element(a, round(anova.xdf$'Sum Sq'[2], digits=3))
a<-table.element(a, round(anova.xdf$'Mean Sq'[2], digits=3))
a<-table.element(a, ' ')
a<-table.element(a, ' ')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='regressionplot.png')
plot(Y~ X, data=xdf, xlab=V2, ylab=V1, main='Regression Solution')
if(intercept == TRUE) abline(coef(lmxdf), col='red')
if(intercept == FALSE) abline(0.0, coef(lmxdf), col='red')
dev.off()
library(car)
bitmap(file='residualsQQplot.png')
qq.plot(resid(lmxdf), main='QQplot of Residuals of Fit')
dev.off()
bitmap(file='residualsplot.png')
plot(xdf$X, resid(lmxdf), main='Scatterplot of Residuals of Model Fit')
dev.off()
bitmap(file='cooksDistanceLmplot.png')
plot.lm(lmxdf, which=4)
dev.off()